69.16.42 problem 515

Internal problem ID [18302]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
Problem number : 515
Date solved : Thursday, October 02, 2025 at 03:10:15 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }&=-6 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-6*diff(diff(diff(y(x),x),x),x) = -6; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{6 x} c_1}{216}+\frac {x^{3}}{6}+\frac {c_2 \,x^{2}}{2}+c_3 x +c_4 \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 36

ode=D[y[x],{x,4}]-6*D[y[x],{x,3}]==-6; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^3}{6}+c_4 x^2+c_3 x+\frac {1}{216} c_1 e^{6 x}+c_2 \end{align*}

✓ Sympy. Time used: 0.044 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)) + 6,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x + C_{3} x^{2} + C_{4} e^{6 x} + \frac {x^{3}}{6} \]